Salim Bouzebda

Strong Approximations for Multivariate Integrated Empirical Processes: Two-Sample Testing, Change-Point Detection, and Inference with Estimated Parameters

We investigate a broad class of multivariate $p$-fold integrated empirical processes obtained by iterated lower-orthant Stieltjes integration of the empirical distribution function on $[0,1]^d$. After deriving exact structural representations for the corresponding integrated distribution and empirical distribution func...

Bahadur-Kiefer Theory for Empirical and Smoothed Quantiles with Censored Associated Data

Inverse-Probability-Weighted Wavelet Estimation of Regression Derivatives Under Missing-at-Random Responses for Stationary Ergodic Processes

We consider the estimation of partial derivatives of multivariate regression-type functionals from incomplete observations generated by a discrete-time strictly stationary ergodic process. The response variable is subject to a missing-at-random (MAR) mechanism, whereas the covariates are fully observed. Building upon t...

Inverse-Probability-Weighted Kernel Estimation of Regression Derivatives Under Missing-at-Random Responses for Stationary Ergodic Processes

This paper develops asymptotic theory for kernel estimation of density-weighted conditional functionals and regression derivatives when responses are missing at random (MAR) and the observations form a strictly stationary ergodic process. Sequential MAR and positivity identify the complete-data conditional target throu...

Learning Nonparametric Conditional Single-Index U-Processes for Missing Locally Stationary Functional Random Fields with Stochastic Spatial Design

This framework addresses a fundamental asymmetry between the information carried by irregular, locally heterogeneous functional covariates and the selectively observed response tuples and introduces a complete-case leave-tuple-out spatial prediction criterion for bandwidth selection and proves oracle optimality over ad...

Asymptotic Normality of Wavelet Density and Regression Estimators Under Censored Ergodic Observations

This paper develops a pointwise distributional theory for linear wavelet density and regression estimation from randomly right-censored observations exhibiting stationary ergodic dependence. In contrast to the prevailing literature, which typically relies on quantitative mixing conditions, our analysis is conducted und...

Asymptotic Theory for Kernel Density Estimation Under Dependent Length-Biased Sampling

We establish an asymptotic theory for the Jones inverse-weighted kernel density estimator when length-biased observations form a strictly stationary short-range dependent sequence. The statistical difficulty is intrinsically composite: reciprocal weighting is singular at the origin, the normalizing mean is estimated fr...

Statistical Learning Theory for Inverse-Probability-Weighted Conditional U-Statistics via Delta Sequences Under Functional Missing-at-Random Models

This paper develops a unified asymptotic theory for inverse-probability-weighted conditional U-statistics of arbitrary fixed order in the presence of missing-at-random responses and infinite-dimensional functional covariates. The target is a conditional higher-order functional generated by a measurable response kernel...